Less emphasis is placed on addition and subtraction in Year 5 as children have grasped the main concepts, but previous work is still developed, and they need to understand that: 716 +  524 is the same as 524 + 716 (this is called the commutative law, but children do not need to know the word!) and that: (25 + 14) + 71 can be worked out in several different orders e.g. 25 + (14 + 71) will give the same answer as the above order. (the associative law) It is important that children have real confidence with adding any two digit numbers (e.g. 42 and 58 ) and that they have a variety of strategies or approaches, depending on the numbers involved - sometimes it is easier to start with the tens, but not always. Constant practice, often not on paper, of these tens and units additions will make larger mental addition much easier. It is expected that children will usually use mental methods to add two digit numbers - NOT write the sum down. Children are also expected to understand that subtraction is the opposite of addition and that it can be used to check addition questions. Where calculators are used the child should make an estimate of the answer first. Children should be able to read, write and understand the following words: Take away,  subtract,  how many are left?,  how much less?,  difference between,  how much more?,  how many more to make?,  decrease, inverse....  and the minus sign (–). They should know that: Subtraction is the same as taking away, finding the difference between and complementary addition. Subtraction is non-commutative. When a larger number is subtracted from a smaller number, the answer is negative. Subtracting a positive number from another makes it smaller. Subtracting zero makes no difference to a number. Subtraction is the inverse of addition. They should have good mental strategies for solving subtraction problems with simple numbers. Children will still need to meet addition and subtraction sums involving 9,  19,  29  etc. or 11,  21,  31  etc. e.g. adding 9,  19,  29 etc by adding 10, 20, 30 etc and then subtracting 1. To subtract 9,   19,   29 etc, in the same way, subtract 10,  20,  30 and then add 1. The same process can be carried out with addition and subtraction of 28,   38,   48 , etc this time adding or subtracting 2 after working out the tens, and, 27,  37,   47 etc by adding or subtracting 3 after working out the tens. For example:   156 - 27 Work out 156 subtract 30 which is 126, then add 3, making 129. In year 5 children are expected to move on from two digit mental arithmetic to three digit and even four digits. It is important to discuss how answers are achieved 'in your head' and explain these methods as they are often very different from doing the same sum on paper. Children should know that if one of the following facts is known, the others can be deduced without further calculation: 275 + 184 = 459        184 + 275 = 459 459 – 184 = 275        459 – 275 = 184 Using easier numbers or numbers with one decimal place, they should be able to calculate one of the combinations mentally and then state the other three. Given a set of numbers such as 629,  255,  682 and 630, they should be able to write down and calculate several combinations of these numbers in addition and subtraction sums, some with just two of the numbers such as 629 + 255 and some with more such as 255 + 682 + 630. They should be able to add together quickly several small numbers such as 5 + 12 + 10  + 7 and should spot pairs of numbers that make 10 or 100. They should also be able to add three multiples of 10 such as 50 + 20 + 70. They should also be able to spot equivalences such as '36 + 38 + 40 + 42 + 44  is the same as five forties'. Lastly, children should be able to explain their methods and show that they have used shortcuts and logical techniques to arrive at their answers. Go to year 5 addition and subtraction concepts